Model Predictive Control (MPC) is an advanced control method that utilizes a model to make predictions about the state evolution for the controlled system, as well as an optimization solver to compute an optimal future control trajectory that satisfies state and control constraints. Inaccuracies in model predictions, caused by modelling errors or external disturbances, significantly hinder the performance of MPC and potentially lead to constraint violations. To address these challenges, Robust MPC (RMPC) explicitly accounts for uncertainties in the model, enhancing the control reliability. Tube-based MPC (TMPC) is a well-known RMPC method, where a nominal MPC generates a reference state trajectory, a tube (i.e., a trajectory of model uncertainties centered around the reference trajectory), and an ancillary control law that ensures the actual states of the system remain within this tube —following the reference trajectory, despite uncertainties.

This thesis presents a critical analysis of current state-of-the-art MPC methods, and proposes novel theoretical developments, architectures, and extensions for effective and computationally efficient handling of uncertainties via MPC . These contributions are rigorously supported by formal proofs. Furthermore, the proposed control frameworks are systematically evaluated through dedicated computer-based simulations, with comparisons drawn against existing methods in terms of optimality, robustness, and computational complexity.

The thesis begins with introducing State-Dependent Dynamic Tube-based MPC (SDD-TMPC), an extension of TMPC designed to more effectively handle the variability of model uncertainties and environmental disturbances. By leveraging available information about state-dependent uncertainties, SDD-TMPC enhances optimality and reduces risks of infeasibility, while maintaining the same level of robustness as TMPC. Although SDD-TMPC demonstrates applicability to systems with varying uncertainties across the state space, its practical implementation is limited by high computational demands.

To mitigate this limitation, Approximate State-Dependent Dynamic Tube-based MPC (ASDDTMPC) is developed. This approach employs Spiking Neural Network (SNN) to approximate the behavior of SDD-TMPC. SNNs were selected for their event-driven processing and biologically inspired efficiency, offering significant advantages for low-power, real-time control. Recognizing that this approximation introduces additional uncertainties, and thus the risk of insufficient robustness to uncertainties, the SDD-TMPC framework is extended to incorporate these approximation errors as additional state-dependent disturbances, thereby preserving robustness. The reduced computational requirements of spiking neural networks enable implementation on resource-constrained platforms, such as small-scale robotic platforms.

Next, the Parent-Child MPC (PC-MPC) architecture is proposed to further reduce computational complexity across a wide range of MPC frameworks. Compatible with both tube-based and deterministic MPC, the PC-MPC architecture decomposes the optimization problem into two linked problems: The Parent MPC (P-MPC) addresses long-term stability and constraint satisfaction, while the Child MPC (C-MPC) focuses on short-term stability and disturbance rejection. P-MPC communicates additional constraints to C-MPC, which determines and executes control strategies. This hierarchical approach, which guarantees robustness and stability, is extendable to systems with complex dynamics and large scales. This is done by incorporating additional Parent layers to further manage computational complexity in such systems.

While robustness is critical, there are environments where maintaining strict constraint satisfaction is infeasible due to the nature and extent of uncertainties. To address this, a new theoretical framework called Fuzzy-Logic-based MPC (FLMPC) is developed, particularly suited for controlling multi-agent systems with imperfect environmental perception operating in unknown environments. FLMPC uses fuzzy vectors to model uncertainties, where each element—being a fuzzy variable—represents the degree to which a region exhibits properties such as “dangerous” or “certain”. Fuzzy maps are constructed by grouping fuzzy vectors. FLMPC performs fuzzy optimization to compute optimal trajectories for all agents, demonstrating superior performance and reduced computational complexity compared to state-of-the-art control methods. This efficiency is achieved by enabling the execution of computationally intensive tasks of fuzzy map generation outside the real-time optimization loop. This is made possible by inheriting the fundamental strength of fuzzy logic, particularly its ability to handle uncertainties over a continuum of values, rather than discrete thresholds. This allows for reliable decision-making based on fuzzy maps within a flexible computational window, rather than being restricted to a specific time step.

The inherent limitation of finite prediction horizons in MPC poses a challenge for exploring tasks in large-scale environments. To improve scalability, a bi-level FLMPC framework—leveraging the PC-MPC architecture in the context of FLMPC — is introduced, with potential for extension to multi-level hierarchies. The Parent Fuzzy-Logic-based MPC (P-FLMPC) formulates a global plan using comprehensive environmental knowledge, while the Child Fuzzy-Logic-based MPC (C-FLMPC) focuses on local enhancement and execution of the plan, retaining flexibility for real-time adaptation.
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Exploring unknown environments and locating multiple targets with multi-robot teams remains challenging due to uncertainty about such environments and the high computational cost of existing planning methods. Model Predictive Control (MPC) is a widely used and effective approach for planning under constraints; however, traditional MPC relies on Bayesian representations and stochastic cost functions, which limit scalability and decision-making horizons in complex search scenarios. This paper introduces fuzzy-logic-based model predictive control (FLMPC), integrated with dynamic fuzzy maps of the environment, to emulate human-like reasoning and to simplify optimization, while preserving and leveraging the predictive structure of MPC and its systematic handling of constraints within the decision-making loop. Building on this foundation, we present a multi-robot exploration framework based on FLMPC for efficient target search in unknown environments. Instead of optimizing stochastic cost functions, FLMPC uses fuzzy abstractions of environmental attributes, such as passability and certainty, derived from probability distributions and local observations. This approach enables longer-horizon planning and efficient handling of multiple objectives. To enhance coordination among robots, FLMPC is extended into a bi-level parent–child architecture, where a high-level parent controller guides global exploration while local child controllers handle short-term planning. This structure not only improves coordination, but also increases robustness to environmental uncertainty thanks to combining long-term strategic decisions with reactive local adjustments that allow handling unexpected changes and environmental uncertainties more effectively. Extensive simulations in unknown 2D environments with randomly placed obstacles and human targets evaluate the proposed FLMPC framework embedded within a parent-child architecture against conventional MPC with stochastic cost functions. Results demonstrate up to 50× faster optimization and significantly improved search performance under environmental uncertainty, positioning FLMPC as a scalable and efficient planning method for large-scale search-and-rescue missions that require coordinated multi-robot exploration. ... Read more

This paper introduces a novel hierarchical model predictive control (MPC) framework, called the Parent–Child MPC architecture, designed to ensure recursive feasibility without relying on terminal constraints. The proposed architecture targets nonlinear constrained systems with Lipschitz continuous dynamics, such as quadrotors, helicopters and autonomous bicycles. For such systems, traditional MPC approaches may suffer from computational intractability or conservativeness due to needing terminal constraints. The proposed framework couples a small-horizon, high-fidelity Child MPC with one or more large-horizon, simplified Parent MPC layers. The Parent layers provide robust invariant tubes that replace terminal constraints, enabling scalable planning and stability guarantees. Two case studies, including a linear double integrator system and a nonlinear system, demonstrate the effectiveness of the architecture. Compared to standard robust tube-based MPC, the Parent–Child MPC achieves up to an eight-fold reduction in solver time and a three-fold increase in controllable prediction horizon. It also maintains performance within 3% of robust tube-based MPC. These results highlight the potential of this architecture for real-time control of complex, nonlinear systems under uncertainty. ... Read more

Manned and unmanned air traffic is experiencing rapid growth. The basis for the safety of flight operations is its reliable surveillance. In addition to primary and secondary radar, modern systems based on satellite positioning play a key role in air traffic control. An important addition to the above systems is multilateration (MLAT). The majority of existing MLAT algorithms operate under the assumption that only the time difference of arrival (TDOA) is available for consideration. However, in scenarios that are more reflective of reality, altitude measurements are also typically included. In this study, we not only extend an existing algorithm to accommodate these additional data points but also derive insights into how the accuracy of measurements is influenced by the incorporation of supplementary information. An important part of this contribution is the software, which, by solving nonlinear optimization problems, allows for the analysis of the distribution of MLAT stations while ensuring the smallest possible measurement uncertainties. ... Read more

Most real-world systems are affected by external disturbances, which may be impossible or costly to measure. For instance, when autonomous robots move in dusty environments, the perception of their sensors is disturbed. Moreover, uneven terrains can cause ground robots to deviate from their planned trajectories. Thus, learning the external disturbances and incorporating this knowledge into the future predictions in decision-making can significantly contribute to improved performance. Our core idea is to learn the external disturbances that vary with the states of the system, and to incorporate this knowledge into a novel formulation for robust tube model predictive control (TMPC). Robust TMPC provides robustness to bounded disturbances considering the known (fixed) upper bound of the disturbances, but it does not consider the dynamics of the disturbances. This can lead to highly conservative solutions. We propose a new dynamic version of robust TMPC (with proven robust stability), called state-dependent dynamic TMPC (SDD-TMPC), which incorporates the dynamics of the disturbances into the decision-making of TMPC. In order to learn the dynamics of the disturbances as a function of the system states, a fuzzy model is proposed. We compare the performance of SDD-TMPC, MPC, and TMPC via simulations, in designed search-and-rescue scenarios. The results show that, while remaining robust to bounded external disturbances, SDD-TMPC generates less conservative solutions and remains feasible in more cases, compared to TMPC. ... Read more

Model Predictive Control (MPC) optimizes an objective function within a prediction window under constraints. In the presence of bounded disturbances, robust versions are used. Recently, a promising robust MPC was introduced that outperforms SOTA approaches. However, solving the optimization problem online is computationally expensive. An efficient approximation method, such as neural networks (NN), can be substituted to accelerate the online computation. There are discrepancies between the control inputs due to the approximation. We propose to model them as bounded state-dependent disturbances to robustly control nonlinear wheeled robots. We consider a spiking NN to ensure that small robots could use it. ... Read more